You have the following grade and step system. People receive a step increase upon reaching their anniversary date in their classification. On promotion, a person receives the same step in the new classification as they held in the old classification.

Joe is hired on $7-1-20$ at Step $2$ in Grade $1$ and is promoted to grade $2$ on $10-1-21$ and to grade $3$ on $4-1-22.$ Show the wage changes. $(8$ points$)$

GRADE $1$

STEP $1$ STEP $2$ STEP $3$ STEP $4$ STEP $5$

$89101112$

$910111213$

$1-1-221011121314$

GRADE $2$

STEP $1$ STEP $2$ STEP $3$ STEP $4$ STEP $5$

$1-1-20910111213$

$1-1-211011121314$

$1-1-221112131415$

GRADE $3$

STEP $1$ STEP $2$ STEP $3$ STEP $4$ STEP $5$

$1-1-201011121314$

$1-1-211112131415$

$1-1-221213141516$